In this paper, we discussed population model of two competing populations with non-linear double diffusion and variable density which described by nonlinear system of competing individuals. We identify new properties,...In this paper, we discussed population model of two competing populations with non-linear double diffusion and variable density which described by nonlinear system of competing individuals. We identify new properties, such as finite speed of propagation, and localization of the outbreaks in a specific area.展开更多
In this paper,we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method(FNDM).The proposed method is a graceful blend of decomposition ...In this paper,we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method(FNDM).The proposed method is a graceful blend of decomposition scheme with natural transform,and three examples are considered to validate and illustrate its efficiency.The nature of FNDM solution has been captured for distinct arbitrary order.In order to illustrate the proficiency and reliability of the considered scheme,the numerical simulation has been presented.The obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology.展开更多
The nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achieved for the first time in the framwork of the Paul-Painlevéappro...The nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achieved for the first time in the framwork of the Paul-Painlevéapproach method(PPAM).When the variables appearing in the exact solutions take specific values,the solitary wave solutions will be easily obtained.The realized results prove the efficiency of this technique.展开更多
文摘In this paper, we discussed population model of two competing populations with non-linear double diffusion and variable density which described by nonlinear system of competing individuals. We identify new properties, such as finite speed of propagation, and localization of the outbreaks in a specific area.
文摘In this paper,we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method(FNDM).The proposed method is a graceful blend of decomposition scheme with natural transform,and three examples are considered to validate and illustrate its efficiency.The nature of FNDM solution has been captured for distinct arbitrary order.In order to illustrate the proficiency and reliability of the considered scheme,the numerical simulation has been presented.The obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology.
文摘The nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achieved for the first time in the framwork of the Paul-Painlevéapproach method(PPAM).When the variables appearing in the exact solutions take specific values,the solitary wave solutions will be easily obtained.The realized results prove the efficiency of this technique.
